To fill the gap in the literature of Bayesian inference, we propose a method for estimating covariance structures under spike and slab prior which uses a mixture of point-mass and normal distribution and exponential prior on off-diagonal entries and diagonal entries of covariance matrices, respectively, which is a modified version of the prior in [1]}. To overcome the limitations of the current Bayesian inference on sparse covariance matrices we have described, we propose a method that uses Laplace approximation to compute posterior probabilities of covariance structures, generates MCMC samples of graphs using Metropolis-Hastings algorithm proposed by [2]} and chooses the model either by median probability model (MPM) or maximum a posteriori (MAP). We estimate covariance matrix by the model of conditional posterior of covariance matrix given the structure.
